The global ocean has taken up a large fraction of the CO<sub>2</sub> released by human activities since the industrial revolution. Quantifying the oceanic anthropogenic carbon (C<sub>ant</sub>) inventory and its variability is important for predicting the future global carbon cycle. The detailed comparison of data-based and model-based estimates is essential for the validation and continued improvement of our prediction capabilities. So far, three global estimates of oceanic C<sub>ant</sub> inventory that are "data-based" and independent of global ocean circulation models have been produced: one based on the Δ C* method, and two that are based on constraining surface-to-interior transport of tracers, the TTD method and a maximum entropy inversion method (GF). The GF method, in particular, is capable of reconstructing the history of C<sub>ant</sub> inventory through the industrial era. In the present study we use forward model simulations of the Community Climate System Model (CCSM3.1) to estimate the C<sub>ant</sub> inventory and compare the results with the data-based estimates. We also use the simulations to test several assumptions of the GF method, including the assumption of constant climate and circulation, which is common to all the data-based estimates. Though the integrated estimates of global C<sub>ant</sub> inventories are consistent with each other, the regional estimates show discrepancies up to 50 %. The CCSM3 model underestimates the total C<sub>ant</sub> inventory, in part due to weak mixing and ventilation in the North Atlantic and Southern Ocean. Analyses of different simulation results suggest that key assumptions about ocean circulation and air-sea disequilibrium in the GF method are generally valid on the global scale, but may introduce errors in C<sub>ant</sub> estimates on regional scales. The GF method should also be used with caution when predicting future oceanic anthropogenic carbon uptake.